basix::quadrature Namespace Reference

Quadrature rules. More...

Enumerations
enum class	type {   Default = 0 , gauss_jacobi = 1 , gll = 2 , xiao_gimbutas = 3 ,   zienkiewicz_taylor = 20 , keast = 21 , strang_fix = 22 }
	Quadrature type.

Functions
template<std::floating_point T>
std::array< std::vector< T >, 2 >	gauss_jacobi_rule (T a, int m)
	Get the Gauss-Jacobi rule for the interval for integrating f(x) * (1-x)^a on the interval [0, 1].
template<std::floating_point T>
std::array< std::vector< T >, 2 >	make_quadrature (const quadrature::type rule, cell::type celltype, polyset::type polytype, int m)
	Make a quadrature rule on a reference cell.
quadrature::type	get_default_rule (cell::type celltype, int m)
	Get the default quadrature type for the given cell and order.
template<std::floating_point T>
std::vector< T >	get_gll_points (int m)
	Get Gauss-Lobatto-Legendre (GLL) points on the interval [0, 1].
template<std::floating_point T>
std::vector< T >	get_gl_points (int m)
	Get Gauss-Legendre (GL) points on the interval [0, 1].

Detailed Description

Quadrature rules.

Function Documentation

gauss_jacobi_rule()

template<std::floating_point T>

std::array< std::vector< T >, 2 > basix::quadrature::gauss_jacobi_rule	(	T	a,
		int	m )

Get the Gauss-Jacobi rule for the interval for integrating f(x) * (1-x)^a on the interval [0, 1].

Template Parameters

The	floating point type.

Parameters

[in]	a	The exponent a.
[in]	m	The number of points.

Returns

Points and weights of a Gauss-Jacobi rule.

make_quadrature()

template<std::floating_point T>

std::array< std::vector< T >, 2 > basix::quadrature::make_quadrature	(	const quadrature::type	rule,
		cell::type	celltype,
		polyset::type	polytype,
		int	m )

Make a quadrature rule on a reference cell.

Template Parameters

T	The floating point type.

Parameters

[in]	rule	Type of quadrature rule (or use quadrature::Default).
[in]	celltype	Cell type.
[in]	polytype	Polyset type.
[in]	m	Maximum degree of polynomial that this quadrature rule will integrate exactly.

Returns

List of points and list of weights. The number of points arrays has shape (num points, gdim).

get_default_rule()

quadrature::type basix::quadrature::get_default_rule	(	cell::type	celltype,
		int	m )

Get the default quadrature type for the given cell and order.

Parameters

[in]	celltype	Cell type.
[in]	m	Maximum degree of polynomial that this quadrature rule will integrate exactly.

Returns

Quadrature type that will be used by default.

get_gll_points()

template<std::floating_point T>

std::vector< T > basix::quadrature::get_gll_points

(

int

m

)

Get Gauss-Lobatto-Legendre (GLL) points on the interval [0, 1].

Template Parameters

T	The floating point type.

Parameters

[in]

m

Number of points.

Returns

Array of GLL points.

get_gl_points()

template<std::floating_point T>

std::vector< T > basix::quadrature::get_gl_points

(

int

m

)

Get Gauss-Legendre (GL) points on the interval [0, 1].

Template Parameters

T	The floating point type.

Parameters

[in]

m

Number of points

Returns

Array of GL points.